The Seventh Seal is well worth watching, as is Goddard's "Breathless," as is Trauffaut's "400 Blows," as is "The Bicycle Thief," "The Battleship Potemkin," and Fritz Lang's "Metropolis"
For anyone studying film, these are the basic building blocks of an understanding of modern film language. That isn't to say that these are films that I like, personally I'm not fond of the Seventh Seal or of Breathless.
However, this is my short list of "old films" that I think are stunning (these films are also great to drop into essays)
Kurosawa - Seven Samurai, Hidden Fortress and Living
Murnae - Faust
Leni Refrenstahl - Olympiad (I know she was a Nazi, but she was also one of the world's greatest film editors)
Fritz Lang - M
plus
Anything by Hitchcock
Sidney Lumet's 12 Angry Men
and finally "To Kill a Mocking Bird" and "Harvey"
Harvey is my favorite, because James Stewart's performance in it is flawless. There had never been a greater film actor.